The American Museum of Natural History has long been on the front lines of the climate change discussion, as its scientists study the potential damage and its educators try to alert new generations to the dangers of global warming.

The depth of that mission is evident in the numerous exhibitions at this Manhattan museum, like the film “Wonders of the Arctic,” which is on view through March 2. “The polar bear has always been the symbol of the Arctic,” the narrator intones. “Now it’s become the face of climate change and the threat it poses.”

But one of the museum’s leaders, a trustee who is also an important donor to the institution, Rebekah Mercer, has been using her family’s millions to fund organizations that question climate change, a cornerstone of the conservative agenda she is advancing as an influential member of President-elect Donald J. Trump’s transition team.

In recent years the Mercer Family Foundation — which Ms. Mercer operates with her father, the New York investor Robert Mercer — has given nearly $8 million to organizations including the Heartland Institute in Illinois, a group that rejects the scientific consensus on climate change. She is also on the board of the Heritage Foundation, a conservative think tank that is skeptical of whether human behavior causes climate change.

The connection of Ms. Mercer, the museum and the Mercer Family Foundation’s donation history came to light during an analysis by The New York Times of activities by cultural leaders who donated to Mr. Trump’s presidential campaign. Several of them are board members at New York City arts organizations, including John Paulson at the Metropolitan Museum of Art and Mercedes T. Bass at the Metropolitan Opera. But none are as unusual a fit as Ms. Mercer and the American Museum of Natural History.

On one level, she is the sort of trustee museums and other nonprofit arts groups compete for: a deep-pocketed donor whose board membership could lead to more contributions. Museums regularly ask major donors to become trustees — particularly those as generous as Ms. Mercer, whose foundation has donated at least $3 million to the museum over the past few years.

Museum leaders generally do not vet donors and trustees for their personal or political views or apply ideological litmus tests. But more often than not, trustees champion the missions and philosophical underpinnings of their museums.

Since Ms. Mercer has only recently emerged as a high-profile player in the Republican Party, bringing her charitable giving new public attention, it’s likely that the museum’s trustees were unaware of her philanthropic history — and specifically, her generous funding of organizations on the forefront of climate change skepticism — when she joined the board in 2013. About a dozen other trustees at the American Museum of Natural History contacted for comment declined or did not respond.

Moreover, institutions with boards as large as the museum’s (which numbers 49) are typically run by a core group of highly active trustees, with others often being less knowledgeable about the detailed backgrounds of fellow members.

It is unclear what, if any, influence Ms. Mercer has had at the museum beyond her financial leverage and her power as a board member. Ms. Mercer did not respond to multiple requests for comment, and Ellen V. Futter, the museum’s president, declined to comment about Ms. Mercer. But Ms. Futter was emphatic that it is the museum’s scientists, not its trustees, who make decisions about the substance of what is presented at the museum.

“The scientists at the museum are the ones who are responsible for the interpretation and presentation of scientific content,” she said.

“We’ve done several exhibits on climate change, we’ve done numerous education offerings on climate change,” she added, “and it is the scientists who make all of the decisions about science.”

Ms. Futter would not comment on the calls for Ms. Mercer to step down or what brought her to the board, declining to discuss the activities of a specific trustee.

Told of Ms. Mercer’s role on the museum board, several scientists and environmental organizations said that she should resign or be removed from her position because, they said, she was working at cross purposes with its mission.

“There is no room for promoters of anti-science on the board of a science museum, let alone arguably the greatest science museum in the world,” said Michael E. Mann, a leader in the climate field who directs the Earth System Science Center at Penn State. He added that Ms. Mercer “has actively funded the climate change denial and disinformation campaign.”

The climate change positions of people surrounding Mr. Trump are being closely scrutinized as he takes office, partly because the president-elect has described climate change as a hoax, and vowed to “cancel” the Paris climate accord and to undo President Obama’s Clean Power Plan.

During the campaign, Ms. Mercer was one of Mr. Trump’s biggest donors, eventually joining his 16-person transition team, in which she played a significant part in pushing forward one climate change skeptic for the cabinet: Jeff Sessions, the nominee for attorney general.

“She’s certainly a force,” the former House Speaker Newt Gingrich, a top Trump adviser, said. “She’s one of the people whose phone calls get taken.”

Environmental concerns prompted climate scientists and other groups last year to call for removal of the conservative philanthropist David H. Koch from the museum’s board. He stepped down, though the museum said the reasons were unrelated to the protests.

Ms. Mercer is not known for publicly speaking out on the climate change issue. But her generous support of organizations that raise doubts about global warming drew criticism from environmental groups like the Sierra Club and Greenpeace.

“To politicize science is shameful; to politicize the institutions that are designed to foster greater learning is even worse,” Michael Brune, executive director of the Sierra Club, said. The museum’s executives “should acknowledge that they have a healthy endowment — a steady stream of funding — and they should thank Ms. Mercer for her service and talk about a reasonable plan for her to resign,” he said.

Jesse Coleman, a researcher with Greenpeace, called Ms. Mercer’s role on the board troubling. “They’re an educational institution and they are trying to present the truth,” he said, “and now they have people in important positions on their board who are actively funding misinformation and they know that.”

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A 2008 exhibition at the American Museum of Natural History explaining the shrinking Arctic ice cap.CreditLibrado Romero/The New York Times

In addition to the Heartland Institute and the Heritage Foundation, the Mercer foundation has made significant donations to the Cato Institute and the Oregon Institute of Science and Medicine, both of which also challenge aspects of climate change.

The Oregon Institute, which does research on biochemistry and diagnostic medicine, was co-founded by Arthur B. Robinson, a chemistry professor who unsuccessfully ran for Congress in Oregon and received $15,000 in campaign contributions from Ms Mercer. In 1997, Mr. Robinson was co-author of an op-ed piece in The Wall Street Journal, “Global Warming Is a Myth,” which called rising levels of carbon dioxide “a boon for the environment.”

The article was a rebuttal to the Kyoto Protocol, which embraced the existence of human-caused global warming and set goals for worldwide emissions reductions. “There is not a shred of persuasive evidence that humans have been responsible for increasing global temperatures,” the piece said, adding, “So we needn’t worry about human use of hydrocarbons warming the Earth.”

Mr. Robinson also directed the Oregon Institute’s Petition Project, which said “that the human-caused global warming hypothesis is without scientific validity and that government action on the basis of this hypothesis would unnecessarily and counterproductively damage both human prosperity and the natural environment.”

Ms. Mercer has science bona fides, having earned a master’s degree in management science and engineering from Stanford University, where she studied biology and math as an undergraduate.

Her father worked for IBM before joining the successful hedge fund, Renaissance Technologies, where he became a chief executive in 2010. Though she briefly worked on Wall Street, Ms. Mercer — along with her sisters, Jenji and Heather Sue (their mother is Diana) — in 2006 purchased the Manhattan bakery Ruby et Violette, which now operates online.

During the recent presidential campaign, Ms. Mercer started as a leading supporter of Ted Cruz, who also argued that the threat of global warming was overstated. She and her husband, Sylvain Mirochnikoff, a managing director at Morgan Stanley — they have four children — hosted a fund-raiser for Mr. Cruz in 2015 at their Upper West Side triplex in Heritage at Trump Place.

Among the biggest Mercer beneficiaries is the Heartland Institute, to which their foundation has given nearly $5 million. In 2011, Joseph Bast, president and chief executive of the institute, wrote that liberals accept global warming as true because stopping it “requires higher taxes, more income redistribution” and other “policies already on the liberal political agenda.”

“Liberals have no reason to ‘look under the hood’ of the global warming scare, to see what the real science says,” he added. “They believe in global warming because they feel it justifies their ideological convictions.”

Beka Economopoulos is founding director of a mobile project called the Natural History Museum, which in 2015 drafted a letter signed by scientists calling for institutions of science and natural history to “cut all ties” with fossil fuel companies. She said she found it troubling that Ms. Mercer held a governing role at the museum despite her support for groups that oppose its efforts.

“How can a science museum reconcile placing a climate denier in a leadership position?” she said. “It’s incomprehensible.”

“In the anti-knowledge era,” Ms. Economopoulos added, “the role of our most trusted institutions of science is more important than ever.”

Colin Moynihan and Agustin Armendariz contributed reporting.

A version of this article appears in print on , on Page C1 of the New York edition with the headline: A Museum Trustee’s Unlikely Priorities. Order Reprints | Today’s Paper | Subscribe